Angular sensitivity of Brewster-angle reflection polarizers: an analytical treatment

The angular sensitivity of Brewster-angle reflection polarizers (BARP) is first studied approximately by determining the Taylor series expansion of the parallel reflectance R(p) as a function of angle of incidence ø near the Brewster angle ø(B). Subsequently, exact and explicit equations are derived that determine the lower and upper limits, ø(l) and ø(u), of the range of ø, that includes ø(B), over which R(p) or the extinction ratio ER is below a stated limit L. Examples are given of Ge and Si IR BARP for which ø(l) and ø(u) are calculated for L from 10(-6) to 10(-1) in ascending multiplicative steps of 10.